It is not obvious whether the world is analogue or binary, continuous or discrete. It’s a live question and the subject of a recent essay contest set up by the Foundational Questions Institute.

That said it seems clear that much or our social lives revolves around the assumption that the world is indeed binary. Male or female, black or white, left or right – simple binary oppositions structure our social relationships through and through. Moreover, we live in an era when developments in technology make it abundantly clear that the bifurcation of the universe into one and zero brings great leaps forward. Why do we do this to ourselves? What possible benefit can it confer?

One answer might be that it makes things simpler, thus allowing us to make faster decisions.

The reason Twenty Questions pretty much works as a parlour game is that twenty yes/no answers are all it takes to distinguish between 1,048,576 (220) discrete subjects. This seems to be roughly the high end of a practical taxonomy for personal use. By way of comparison, note that if one was to play the game using English Wikipedia articles it would need to be renamed Twenty-Two Questions to cover the 3,673,861 articles in existence in mid-2011 (222 = 4,194,304).

The promise of information theory, on some accounts, is that we can sort everything in binary terms. In John Wheeler’s well-known formulation, ‘it from bit’:

“It is not unreasonable to imagine that information sits at the core of physics, just as it sits at the core of a computer.

It from bit. Otherwise put, every ‘it’—every particle, every field of force, even the space-time continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. ‘It from bit’ symbolizes the idea that every item of the physical world has at bottom—a very deep bottom, in most instances—an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes–no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe.” (John Archibald Wheeler 1990: 5)

In physics perhaps (more generally, in the ‘ontological basement’, as Paul Davies puts it). But as any one who has ever heard of racism or sexism will recognise, splitting the social world into opposed pairs often makes us get things very, very wrong. Our fondness for quick and dirty social heuristics has a habit of misleading us. Simpler does not by any means equate to more correct. Reality is more complex than a game of Twenty Questions and it takes more than yes/no answers to parse the social.

So it is not surprising that when faced with various kinds of binary sorting mechanism we experience a sense of disappointment. What may have seemed like a good idea – to simplify by means of bifurcation – turns out to produce less than useful information. The left/right dichotomy in politics turns out to be forced and to obscure almost as much as it reveals. Similarly it turns out that gender is a poor indicator of ability to own property or many of the other issues it has historically been used to indicate. And as for skin colour, this seems to produce far more noise than signal…. It is as though the usefulness of binary sorting has got the better of us and instead of recognising its limits we have tried to sort everything in binary terms. The reward is conservation of energy. The cost is accuracy.

What if the cost is too high? A recent example is a paper claiming to provide insights into differences between national cultures on the basis of a distinction between ‘tight’ and ‘loose’ cultures. This is a fairly well-rehearsed but contentious pair of categories that derives from anthropology.

The problem is that the ranking of nations on this basis doesn’t appear to shed much light on the national characteristics in question. Again, what is claimed to be signal looks suspiciously like noise.

I remain to be convinced but in the meantime I want to propose an interim alternative.

Instead of simplifying by means of one bit of information (tight/loose, black/white, male/female, left/right) we should do so by means of at least two bits of information.

It seems to me that a binary choice, between yes and no or between 1 and 0 always implies a set of Boolean operands just waiting to be used. Yes or no always begs the question: Yes and no?

One way of depicting this expanded set of choices is to frame each binary single bit choice as a two bit choice:

YES Yes and not No Yes and No

NOT YES Not Yes and not NoNo and not Yes

NOT NO NO

This is not to suggest that reality actually is made up of two bits, or any other number of bits for that matter, information theorists notwithstanding. Rather, my claim is that if, in seeking to understand the social world, there is indeed a sweet spot somewhere between energy conservation and accuracy, then a two bit heuristic process is closer to that sweet spot than our current dominant but misleading fondness for single bit, yes/no thinking.